乒乓球与球拍之间的摩擦

现代乒乓球运动中几乎所有技术都要借助于摩擦。制造旋转时，球拍与球之间的摩擦主要是静摩擦和滚动摩擦，它们的作用效果互不相同。静摩擦不但使乒乓球产生旋转，也使乒乓球产生平动；滚动摩擦则不利于乒乓球运动中制造旋转。静摩擦与滚动摩擦都是随时间变化的量，且两者的大小与多种因素有关。     

Oblique impact of a tennis ball on the strings of a tennis racket

Measurements are presented of the friction force acting on a tennis ball incident obliquely on the strings of a tennis racket. This information, when combined with measurements of ball speed and spin, reveals details of the bounce process that have not previously been observed and also provides the first measurements of the coefficient of sliding friction between a tennis ball and the strings of a tennis racket. At angles of incidence less than about 40° to the string plane, the ball slides across the strings during the whole bounce period. More commonly, the ball is incident at larger angles in which case the ball slides across the string plane for a short distance before gripping the strings. While the bottom of the ball remains at rest on the strings, the remainder of the ball continues to rotate for a short period, after which the ball suddenly releases its grip and the bottom of the ball slides backwards on the string plane. The bounce angle depends mainly on the angle of incidence and the rotation speed of the incident ball. Differences in bounce angle and spin off head-clamped and hand-held rackets are also described.     

The effect of tennis racket string vibration dampers on racket handle vibrations and discomfort following impacts.

In this study, we evaluated the effect of the use of tennis racket string vibration dampers on racket handle vibrations, and perceptions of hand and arm discomfort experienced by tennis players owing to stationary racket impacts. Twenty tennis players (10 males, 10 females) aged 18-29 years volunteered for the study. Two different racket models were impacted at the geometric centre of the racket face and 100 mm distal to the centre both with and without string vibration dampers in place. The participants could neither see nor hear the impacts, and they indicated their discomfort immediately after each impact using a visual analogue scale. An analysis of variance (2 x 2 x 2 factorial) was performed on the scaled discomfort ratings with the factors damping condition, racket type and impact location. No significant differences in discomfort ratings between damped and undamped impacts or between the two racket types were found. Also, central impacts were found to be more comfortable than impacts 100 mm distal to the centre (P< 0.05). There were no significant interaction effects. Vibration traces from an accelerometer mounted on the racket handle revealed that string vibration dampers quickly absorbed high-frequency string vibration without attenuating the lower-frequency frame vibration. In conclusion, we found no evidence to support the contention that string vibration dampers reduce hand and arm impact discomfort.     

A review of tennis racket performance parameters

The application of advanced engineering to tennis racket design has influenced the nature of the sport. As a result, the International Tennis Federation has established rules to limit performance, with the aim of protecting the nature of the game. This paper illustrates how changes to the racket affect the player-racket system. The review integrates engineering and biomechanical issues related to tennis racket performance, covering the biomechanical characteristics of tennis strokes, tennis racket performance, the effect of racket parameters on ball rebound and biomechanical interactions. Racket properties influence the rebound of the ball. Ball rebound speed increases with frame stiffness and as string tension decreases. Reducing inter-string contacting forces increases rebound topspin. Historical trends and predictive modelling indicate swingweights of around 0.030–0.035 kg/m² are best for high ball speed and accuracy. To fully understand the effect of their design changes, engineers should use impact conditions in their experiments, or models, which reflect those of actual tennis strokes. Sports engineers, therefore, benefit from working closely with biomechanists to ensure realistic impact conditions.     

Effect of string bed pattern on ball spin generation from a tennis racket

Topspin has become a vital component of modern day tennis. Ball-to-string bed and inter-string friction coefficients can affect topspin generation from a racket. The aim of this research was to determine the effect of string bed pattern on topspin generation. Tennis balls were projected onto nine head-clamped rackets with different string bed patterns. The balls were fired at 24 m/s, at an angle of 26° to the string bed normal with a backspin rate of 218 rad/s and outbound velocity, spin and angle were measured. Outbound velocity was shown to be independent of string bed pattern. Outbound angle increased with the number of cross strings, while outbound topspin decreased. In the most extreme case, decreasing the number of cross strings from 19 to 13 increased rebound topspin from 117 to 170 rad/s.     

Effect of skill decomposition on racket and ball kinematics of the elite junior tennis serve

Whole body kinematics of the tennis serve have been reported extensively in the literature, yet comparatively less information exists regarding the kinematic characteristics of the swing and toss. In attempting to develop consistency in placement of the toss and racket trajectory, coaches will often decompose the serve and practice it in separate parts. A 22-camera VICON MX motion analysis system, operating at 250 Hz, captured racket, ball and hand kinematics of the serves of five elite junior players under three conditions. The conditions were flat first serves (FS) directed to a 1 x 1 m target bordering the 'T' of the deuce service box, a ball toss (BT) in isolation and a free swing (SW) in isolation. Players were instructed to perform BT and SW as in the FS. Paired t-tests assessed within-group differences in hand, racket and ball kinematics between the discrete skill and the two decomposed conditions. Vertical displacement of the ball at its zenith increased significantly during BT compared with the FS and temporal associations between racket and ball motion during the FS (r = 0.861) were affected during task decomposition. This study questions the pervasive use of task decomposition in the development of the tennis serve.     

Effect of skill decomposition on racket and ball kinematics of the elite junior tennis serve

Whole body kinematics of the tennis serve have been reported extensively in the literature, yet comparatively less information exists regarding the kinematic characteristics of the swing and toss. In attempting to develop consistency in placement of the toss and racket trajectory, coaches will often decompose the serve and practice it in separate parts. A 22-camera VICON MX motion analysis system, operating at 250 Hz, captured racket, ball and hand kinematics of the serves of five elite junior players under three conditions. The conditions were flat first serves (FS) directed to a 1 × 1 m target bordering the ‘T’ of the deuce service box, a ball toss (BT) in isolation and a free swing (SW) in isolation. Players were instructed to perform BT and SW as in the FS. Paired t-tests assessed within-group differences in hand, racket and ball kinematics between the discrete skill and the two decomposed conditions. Vertical displacement of the ball at its zenith increased significantly during BT compared with the FS and temporal associations between racket and ball motion during the FS (r = 0.861) were affected during task decomposition. This study questions the pervasive use of task decomposition in the development of the tennis serve.     

Comparison of a finite element model of a tennis racket to experimental data

Modern tennis rackets are manufactured from composite materials with high stiffness-to-weight ratios. In this paper, a finite element (FE) model was constructed to simulate an impact of a tennis ball on a freely suspended racket. The FE model was in good agreement with experimental data collected in a laboratory. The model showed racket stiffness to have no influence on the rebound characteristics of the ball, when simulating oblique spinning impacts at the geometric stringbed centre. The rebound velocity and topspin of the ball increased with the resultant impact velocity. It is likely that the maximum speed at which a player can swing a racket will increase as the moment of inertia (swingweight) decreases. Therefore, a player has the capacity to hit the ball faster, and with more topspin, when using a racket with a low swingweight.     

The effect of ball impact location on racket and forearm joint angle changes for one-handed tennis backhand groundstrokes

Recreational tennis players tend to have higher incidence of tennis elbow, and this has been hypothesised to be related to one-handed backhand technique and off-centre ball impacts on the racket face. This study aimed to investigate for a range of participants the effect of off-longitudinal axis and off-lateral axis ball–racket impact locations on racket and forearm joint angle changes immediately following impact in one-handed tennis backhand groundstrokes. Three-dimensional racket and wrist angular kinematic data were recorded for 14 university tennis players each performing 30 “flat” one-handed backhand groundstrokes. Off-longitudinal axis ball–racket impact locations explained over 70% of the variation in racket rotation about the longitudinal axis and wrist flexion/extension angles during the 30 ms immediately following impact. Off-lateral axis ball–racket impact locations had a less clear cut influence on racket and forearm rotations. Specifically off-longitudinal impacts below the longitudinal axis forced the wrist into flexion for all participants with there being between 11° and 32° of forced wrist flexion for an off-longitudinal axis impact that was 1 ball diameter away from the midline. This study has confirmed that off-longitudinal impacts below the longitudinal axis contribute to forced wrist flexion and eccentric stretch of the wrist extensors and there can be large differences in the amount of forced wrist flexion from individual to individual and between strokes with different impact locations.     

Subject-specific computer simulation model for determining elbow loading in one-handed tennis backhand groundstrokes

A subject-specific angle-driven computer model of a tennis player, combined with a forward dynamics, equipment-specific computer model of tennis ball-racket impacts, was developed to determine the effect of ball-racket impacts on loading at the elbow for one-handed backhand groundstrokes. Matching subject-specific computer simulations of a typical topspin/slice one-handed backhand groundstroke performed by an elite tennis player were done with root mean square differences between performance and matching simulations of < 0.5 degrees over a 50 ms period starting from ball impact. Simulation results suggest that for similar ball-racket impact conditions, the difference in elbow loading for a topspin and slice one-handed backhand groundstroke is relatively small. In this study, the relatively small differences in elbow loading may be due to comparable angle-time histories at the wrist and elbow joints with the major kinematic differences occurring at the shoulder. Using a subject-specific angle-driven computer model combined with a forward dynamics, equipment-specific computer model of tennis ball-racket impacts allows peak internal loading, net impulse, and shock due to ball-racket impact to be calculated which would not otherwise be possible without impractical invasive techniques. This study provides a basis for further investigation of the factors that may increase elbow loading during tennis strokes.     

A three-dimensional analysis of the contributions of upper limb joint movements to horizontal racket head velocity at ball impact during tennis serving

In this study, we examined the relationship between upper limb joint movements and horizontal racket head velocity to clarify joint movements for developing racket head speed during tennis serving. Sixty-six male tennis players were videotaped at 200 Hz using two high-speed video cameras while hitting high-speed serves. The contributions of each joint rotation to horizontal racket velocity were calculated using vector cross-products between the angular velocity vectors of each joint movement and relative position vectors from each joint to the racket head. Major contributors to horizontal racket head velocity at ball impact were shoulder internal rotation (41.1%) and wrist palmar flexion (31.7%). The contribution of internal rotation showed a significant positive correlation with horizontal racket head velocity at impact (r = 0.490, P < 0.001), while the contribution of palmar flexion showed a significant negative correlation (r = ? 0.431, P < 0.001). The joint movement producing the difference in horizontal racket head velocity between fast and slow servers was shoulder internal rotation, and angular velocity of shoulder internal rotation must be developed to produce a high racket speed.     

A three-dimensional analysis of the contributions of upper limb joint movements to horizontal racket head velocity at ball impact during tennis serving

In this study, we examined the relationship between upper limb joint movements and horizontal racket head velocity to clarify joint movements for developing racket head speed during tennis serving. Sixty-six male tennis players were videotaped at 200 Hz using two high-speed video cameras while hitting high-speed serves. The contributions of each joint rotation to horizontal racket velocity were calculated using vector cross-products between the angular velocity vectors of each joint movement and relative position vectors from each joint to the racket head. Major contributors to horizontal racket head velocity at ball impact were shoulder internal rotation (41.1%) and wrist palmar flexion (31.7%). The contribution of internal rotation showed a significant positive correlation with horizontal racket head velocity at impact (r = 0.490, P < 0.001), while the contribution of palmar flexion showed a significant negative correlation (r = - 0.431, P < 0.001). The joint movement producing the difference in horizontal racket head velocity between fast and slow servers was shoulder internal rotation, and angular velocity of shoulder internal rotation must be developed to produce a high racket speed.     

Effect of tennis racket parameters on a simulated groundstroke

Composite materials have given manufacturers the freedom to develop a broad range of tennis rackets, allowing them to change key parameters such as the structural stiffness, mass, and position of the balance point. The aim of this research was to determine how changing these parameters could affect ball resultant rebound velocity and spin for a simulated groundstroke. A finite element model of a freely suspended racket and strings was used to determine the effect of racket parameters for oblique spinning impacts at a range of locations on the stringbed. The finite element simulations were conducted in the laboratory frame of reference, where the ball is projected onto an initially stationary racket. The mean rebound velocity of the ball was 9% higher for a structurally stiff racket, 37% higher for a heavy racket, and 32% higher for a head-heavy racket. In addition, the mean rebound topspin of the ball was 23% higher for a heavy racket and 21% higher for a head-heavy racket. Therefore, in relation to a groundstroke with an impact location away from the node, the rebound velocity of the ball is likely to increase with the structural stiffness of a racket. The effect of changing the mass and position of the balance point is more complex, as it is dependent on the relationship between the transverse moment of inertia and maximum pre-impact swing velocity.     

乒乓球正手快攻和弧圈球技术中球拍的运动学特征

对10名乒乓球运动员正手快攻、弧圈球技术(每种技术分中等力量和最大力量两种发力方式)进行测试与分析后发现,重打和重拉的引拍结束时刻的球拍速度分别大于轻打和轻拉.在击球时刻,轻打的速度小于重打,轻拉的速度小于重拉,重打的速度小于重拉;正手弧圈球技术的总时间长于正手快攻技术;拉的幅度大于打的幅度.     

The footprint of a tennis ball

The Hawk-Eye line-calling system in tennis uses a footprint of the ball to determine whether the ball was in or out. However, the footprint itself is not measured. It is the ball trajectory through the air that is measured. Measurements of the footprint are presented in this paper, showing how the high initial rate of expansion of the footprint and other technical difficulties can lead to potential errors in the Hawk-Eye system. The footprint was measured for vertical and oblique impacts, and is compared with recent results presented at a tournament where Hawk-Eye was installed.     

对新型乒乓球性能的计算与研究

据国际乒联透露,为提高乒乓球的观赏性,吸引群众,将把现用乒乓球的直径由３８毫米改为４０毫米,被称为“新型球”或“大球”,并将在１９９７年第４４届世乒赛期间举行一次实验性的大球比赛。为了解大球的性能,探索其可行性,以尽快掌握其运动规律,对大球的参数和性能进行了计算与分析。如果制作大球的材料与小球的相同,计算结果：大球的质量增加０．２７１７克,材料体积增加０．１８８４厘米３,球的体积增大４．７８１厘米３,绕通过质心额状轴为转动惯量增加１．３９１立方厘米。如果用大球比赛,以与击小球同样的方式和大小相等的力来打击大球,大球的转速将比小球减少９．４１转／秒（约减少１／５）,速度减慢４．１４米／秒（约减少１／１０）,但大球的性能发生了明显的变化。     

The effects of player grip on the dynamic behaviour of a tennis racket

The aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player’s grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under “slight”, “medium” and “strong” grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player’s grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket’s dynamic behaviour according to the player’s grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.     

女子乒乓球运动员横拍反手生胶的接发球技术

对4名现役优秀女子横拍反手生胶打法运动员接发球技术进行统计分析,结果显示:4名运动员反手接发球的比例高达93.2%～100%,其命中率高达82.9%～98.0%,但其直接得失分率都很低,分别为0～7.3%和2.0%～17.1%.在处理台内球的技术应用中,弹击技术的使用率均为零,接发球落点位置50%以上都在对方反手位,落点在对方正手位的比例均为零.因此,这几名运动员反手接发球使用率高,侧身正手接发球使用率却很低.反手接发球失误少,但很难直接得分.     

乒乓球击球瞬间球拍形变力的实验研究

在击球时,乒乓球拍会产生一定的形变,其形变的大小反映了球拍受力的大小.运用动态应变测试系统测量了不同技术击球时球拍拍柄根部应变力的大小,结果表明:采用摩擦击球的方式击球,球拍形变幅度较大,获得的形变力也较大;撞击球的方式击球,球拍形变幅度小,震动较大,球拍击球瞬间所受的作用力时间相对较短.     

Carbon outclasses wood in racket paddles: Ratings of expert and intermediate tennis players

Wooden racket paddles were modified with rubber and carbon fibre laminates and their differences tested in terms of flexural, damping, and coefficient of restitution properties. Four rackets types were designed: a wood reference, wood with rubber, carbon fibre 0°, and carbon fibre 90°. Seven expert and eight intermediate tennis players tested the rackets. To determine which of the four rackets suited the players best, we asked the players to compare the rackets two by two. After each pair tested, participants had to fill out a 4-item questionnaire in which different aspects of the rackets' performance were judged. The most preferred racket was the 0° carbon fibre racket, followed by the 90° carbon fibre racket, the wood racket and, finally, the 1-mm rubber racket. Thus, rackets with the highest stiffness, least damping, and highest coefficient of restitution were the most preferred. Interestingly, although experts and intermediate players overall judged the rackets in very similar ways according to force, vibration, and control, they were sensitive to quite different physical characteristics of the rackets.